Rationality

rationality.json

https://arbital.com/p/rationality

by Eliezer Yudkowsky Jul 2 2015 updated Dec 16 2015

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Rationality

The subject domain for [ epistemic] and [ instrumental] rationality.

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Alexei Andreev, Eliezer Yudkowsky

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Bayesian reasoning A probability-theory-based view of the world; a coherent way of changing probabilistic beliefs based on evidence. - Eliezer Yudkowsky

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Stub This page only gives a very brief overview of the topic. If you're able to, please help expand or improve it! - Eliezer Yudkowsky

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Epistemology What is truth? - Eliezer Yudkowsky
- Central examples The "central examples" for a subject are examples that are referred to over and over again in the co… - Eliezer Yudkowsky
- Conceivability A hypothetical scenario is 'conceivable' or 'imaginable' when it is not *immediately* incoherent, al… - Eliezer Yudkowsky
- Fallacies To call something a fallacy is to assert that you think people shouldn't think like that. - Eliezer Yudkowsky
  - Bulverism Bulverism is when you explain what goes so horribly wrong in people's minds when they believe X, before you've actually explained why X is wrong. Forbidden on Arbital. - Eliezer Yudkowsky
  - Emphemeral premises When somebody says X, don't just say, "Oh, not-X because Y" and then forget about Y a day later. Y is now an important load-bearing assumption in your worldview. Write Y down somewhere. - Eliezer Yudkowsky
  - Gotcha button A conversational point which, when pressed, causes the other person to shout "Gotcha!" and leap on what they think is a weakness allowing them to dismiss the conversation. - Eliezer Yudkowsky
  - Harmless supernova fallacy False dichotomies and continuum fallacies which can be used to argue that anything, including a supernova, must be harmless. - Eliezer Yudkowsky
  - Invisible background fallacies Universal laws also apply to objects and ideas that may fade into the invisible background. Reasoning as if these laws didn't apply to less obtrusive concepts is a type of fallacy. - Eliezer Yudkowsky
  - Mind projection fallacy Uncertainty is in the mind, not in the environment; a blank map does not correspond to a blank territory. In general, the territory may have a different ontology from the map. - Eliezer Yudkowsky
  - Multiple stage fallacy You can make an arbitrary proposition sound very improbable by observing how it seemingly requires X, Y, and Z. This didn't work for Nate Silver forecasting the Trump nomination. - Eliezer Yudkowsky
  - Proving too much If your argument could just as naturally be used to prove that Bigfoot exists and that Peano arithmetic is inconsistent, maybe it's an untrustworthy kind of argument. - Eliezer Yudkowsky
- Guarded definition A guarded definition is one where at least one position suspects there will be pressure to stretch a… - Eliezer Yudkowsky
- Intension vs. extension "Red is a light with a wavelength of 700 nm" vs. "Look at this red apple, red car, and red cup." - Eliezer Yudkowsky
- Perfect rolling sphere If you don't understand something, start by assuming it's a perfect rolling sphere. - Eliezer Yudkowsky
- Psychologizing It's sometimes important to consider how other people might be led into error. But psychoanalyzing them is also dangerous! Arbital discussion norms say to explicitly note this as "psychologizing". - Eliezer Yudkowsky
  - Bulverism Bulverism is when you explain what goes so horribly wrong in people's minds when they believe X, before you've actually explained why X is wrong. Forbidden on Arbital. - Eliezer Yudkowsky
- Strained argument A phenomenological feeling associated with a step of reasoning going from X to Y where it feels like… - Eliezer Yudkowsky
- Strictly factual question A "question of strict fact" is one which is true or false about the material universe (and maybe some math) without introducing any issues of values, perspectives, etcetera. - Eliezer Yudkowsky
- The empiricist-theorist false dichotomy No discussion here yet: See https://www.facebook.com/groups/674486385982694/permalink/7846641016315… - Eliezer Yudkowsky
Humans doing Bayes The human use of Bayesian reasoning in everyday life - Eliezer Yudkowsky
- Explicit Bayes as a counter for 'worrying' Explicitly walking through Bayes's Rule can summarize your knowledge and thereby stop you from bouncing around pieces of it. - Eliezer Yudkowsky
Ideological Turing test Can you explain the opposing position well enough that people can't tell whether you or a real advocate of that position created the explanation? - Eliezer Yudkowsky
Introduction to Effective Altruism Effective altruism (EA) means using evidence and reason to take actions that help others as much as … - Aaron Gertler
Probability theory The logic of science; coherence relations on quantitative degrees of belief. - Eliezer Yudkowsky
- Bayesian reasoning A probability-theory-based view of the world; a coherent way of changing probabilistic beliefs based on evidence. - Eliezer Yudkowsky
  - Bayes' rule Bayes' rule is the core theorem of probability theory saying how to revise our beliefs when we make a new observation. - Eliezer Yudkowsky
    - Bayes' rule examples Interesting problems solvable by Bayes' rule - Eliezer Yudkowsky
      - Introductory Bayesian problems Bayesian problems to try to solve yourself, before beginning to learn about Bayes' rule. - Eliezer Yudkowsky
        Blue oysters A probability problem about blue oysters. - Nate Soares
        Diseasitis 20% of patients have Diseasitis. 90% of sick patients and 30% of healthy patients turn a tongue depressor black. You turn a tongue depressor black. What's the chance you have Diseasitis? - Eliezer Yudkowsky
        Sock-dresser search There's a 4/5 chance your socks are in one of your dresser's 8 drawers. You check 6 drawers at random. What's the probability they'll be in the next drawer you check? - Nate Soares
        Sparking widgets 10% of widgets are bad and 90% are good. 4% of good widgets emit sparks, and 12% of bad widgets emit… - Nate Soares
      - Realistic (Math 1) Real-life examples of Bayesian reasoning - Eliezer Yudkowsky
    - Bayes' rule: Beginner's guide Beginner's guide to learning about Bayes' rule. - Alexei Andreev
    - Bayes' rule: Definition Bayes' rule is the mathematics of probability theory governing how to update your beliefs in the lig… - Nate Soares
    - Bayes' rule: Functional form Bayes' rule for to continuous variables. - Eliezer Yudkowsky
    - Bayes' rule: Guide The Arbital guide to Bayes' rule - Eliezer Yudkowsky
      - Bayes' Rule and its different forms This is an arc that includes different ways to look at Bayes' Rule. - Alexei Andreev
      - Bayes' Rule and its implications This is an arc that includes implications of the Bayes's Rule. - Alexei Andreev
      - Comprehensive guide to Bayes' Rule This is an arc that includes all Bayes content. - Alexei Andreev
      - Introduction to Bayes' Rule odds form This is an arc that includes just enough content to teach about Bayes's Rule odds form. - Alexei Andreev
      - Wants to get straight to Bayes A simple requisite page to mark whether the user has selected wanting to get straight into Bayes on … - Eliezer Yudkowsky
    - Bayes' rule: Log-odds form A simple transformation of Bayes' rule reveals tools for measuring degree of belief, and strength of evidence. - Eliezer Yudkowsky
    - Bayes' rule: Odds form The simplest and most easily understandable form of Bayes' rule uses relative odds. - Eliezer Yudkowsky
      - Introduction to Bayes' rule: Odds form Bayes' rule is simple, if you think in terms of relative odds. - Eliezer Yudkowsky
    - Bayes' rule: Probability form The original formulation of Bayes' rule. - Nate Soares
      - Odds form to probability form The odds form of Bayes' rule works for any two hypotheses $H_i$ and $H_j,$ and looks like this: $$\… - Nate Soares
      - Proof of Bayes' rule: Probability form Let $\mathbf H$ be a [random\_variable variable] in $\mathbb P$ for the true hypothesis, and let $H_… - Nate Soares
    - Bayes' rule: Proportional form The fastest way to say something both convincing and true about belief-updating. - Eliezer Yudkowsky
    - Bayes' rule: Vector form For when you want to apply Bayes' rule to lots of evidence and lots of variables, all in one go. (This is more or less how spam filters work.) - Eliezer Yudkowsky
    - Belief revision as probability elimination Update your beliefs by throwing away large chunks of probability mass. - Eliezer Yudkowsky
    - Frequency diagram Visualizing Bayes' rule by manipulating frequencies in large populations - Nate Soares
      - Frequency diagrams: A first look at Bayes The most straightforward visualization of Bayes' rule. - Nate Soares
    - High-speed intro to Bayes's rule A high-speed introduction to Bayes's Rule on one page, for the impatient and mathematically adept. - Eliezer Yudkowsky
    - Path: Multiple angles on Bayes's Rule A learning-path placeholder page for learning multiple angles on Bayes's Rule. - Eliezer Yudkowsky
    - Probability notation for Bayes' rule The probability notation used in Bayesian reasoning - Eliezer Yudkowsky
      - Probability notation for Bayes' rule: Intro (Math 1) How to read, and identify, the probabilities in Bayesian problems. - Eliezer Yudkowsky
    - Proof of Bayes' rule Proofs of Bayes' rule, with graphics - Eliezer Yudkowsky
      - Proof of Bayes' rule: Probability form Let $\mathbf H$ be a [random\_variable variable] in $\mathbb P$ for the true hypothesis, and let $H_… - Nate Soares
    - Shift towards the hypothesis of least surprise When you see new evidence, ask: which hypothesis is *least surprised?* - Nate Soares
    - Waterfall diagram Visualizing Bayes' rule as the mixing of probability streams. - Eliezer Yudkowsky
      - Waterfall diagrams and relative odds A way to visualize Bayes' rule that yields an easier way to solve some problems - Eliezer Yudkowsky
  - Bayesian update Bayesian updating: the ideal way to change probabilistic beliefs based on evidence. - Eliezer Yudkowsky
    - Bayesian view of scientific virtues Why is it that science relies on bold, precise, and falsifiable predictions? Because of Bayes' rule, of course. - Eliezer Yudkowsky
    - Extraordinary claims require extraordinary evidence The people who adamantly claim they were abducted by aliens do provide some evidence for aliens. They just don't provide quantitatively enough evidence. - Eliezer Yudkowsky
      - Extraordinary claims What makes something an 'extraordinary claim' that requires extraordinary evidence? - Eliezer Yudkowsky
    - Ordinary claims require ordinary evidence Extraordinary claims require extraordinary evidence, but ordinary claims *don't*. - Nate Soares
    - Path: Insights from Bayesian updating A learning-path placeholder page for insights derived from the Bayesian rule for updating beliefs. - Eliezer Yudkowsky
    - Strength of Bayesian evidence From a Bayesian standpoint, the strength of evidence can be identified with its likelihood ratio. - Eliezer Yudkowsky
  - Empirical probabilities are not exactly 0 or 1 "Cromwell's Rule" says that probabilities of exactly 0 or 1 should never be applied to empirical propositions - there's always some probability, however tiny, of being mistaken. - Eliezer Yudkowsky
  - Finishing your Bayesian path on Arbital The page that comes at the end of reading the Arbital Guide to Bayes' rule - Eliezer Yudkowsky
  - Humans doing Bayes The human use of Bayesian reasoning in everyday life - Eliezer Yudkowsky
    - Explicit Bayes as a counter for 'worrying' Explicitly walking through Bayes's Rule can summarize your knowledge and thereby stop you from bouncing around pieces of it. - Eliezer Yudkowsky
  - Ignorance prior Key equations for quantitative Bayesian problems, describing exactly the right shape for what we believed before observation. - Eliezer Yudkowsky
    - Inductive prior Some states of pre-observation belief can learn quickly; others never learn anything. An "inductive prior" is of the former type. - Eliezer Yudkowsky
      - Laplace's Rule of Succession Suppose you flip a coin with an unknown bias 30 times, and see 4 heads and 26 tails. The Rule of Succession says the next flip has a 5/32 chance of showing heads. - Eliezer Yudkowsky
      - Solomonoff induction A simple way to superintelligently predict sequences of data, given unlimited computing power. - Eliezer Yudkowsky
        Solomonoff induction: Intro Dialogue (Math 2) An introduction to Solomonoff induction for the unfamiliar reader who isn't bad at math - Eliezer Yudkowsky
      - Universal prior A "universal prior" is a probability distribution containing *all* the hypotheses, for some reasonable meaning of "all". E.g., "every possible computer program that computes probabilities". - Eliezer Yudkowsky
  - Interest in mathematical foundations in Bayesianism "Want" this requisite if you prefer to see extra information about the mathematical foundations in Bayesianism. - Eliezer Yudkowsky
  - Likelihood "Likelihood", when speaking of Bayesian reasoning, denotes *the probability of an observation, sup… - Nate Soares
    - Likelihood function Let's say you have a piece of evidence $e$ and a set of hypotheses $\mathcal H.$ Each $H_i \in \math… - Nate Soares
    - Likelihood notation The likelihood of a piece of evidence $e$ according to a hypothesis $H,$ known as "the likelihood of… - Nate Soares
    - Likelihood ratio Given a piece of evidence $e$ and two hypothsese $H_i$ and $H_j,$ the likelihood ratio between them… - Nate Soares
    - Relative likelihood How relatively likely an observation is, given two or more hypotheses, determines the strength and direction of evidence. - Eliezer Yudkowsky
  - Posterior probability What we believe, after seeing the evidence and doing a Bayesian update. - Eliezer Yudkowsky
  - Prior A state of prior knowledge, before seeing information on a new problem. Potentially complicated. - Eliezer Yudkowsky
  - Prior probability What we believed before seeing the evidence. - Eliezer Yudkowsky
  - Strictly confused A hypothesis is strictly confused by the raw data, if the hypothesis did much worse in predicting it than the hypothesis itself expected. - Eliezer Yudkowsky
  - Subjective probability Probability is in the mind, not in the environment. If you don't know whether a coin came up heads or tails, that's a fact about you, not a fact about the coin. - Eliezer Yudkowsky
    - Probability distribution: Motivated definition People keep writing things like P(sick)=0.3. What does this mean, on a technical level? - Nate Soares
- Mutually exclusive and exhaustive The condition needed for probabilities to sum to 1 - Eliezer Yudkowsky
- Normalization (probability) That thingy we do to make sure our probabilities sum to 1, when they should sum to 1. - Eliezer Yudkowsky
- Odds Odds express a relative probability. - Eliezer Yudkowsky
  - Odds: Introduction What's the difference between probabilities and odds? Why is a 20% probability of success equivalent to 1 : 4 odds favoring success? - Nate Soares
  - Odds: Refresher A quick review of the notations and mathematical behaviors for odds (e.g. odds of 1 : 2 for drawing a red ball vs. green ball from a barrel). - Nate Soares
  - Odds: Technical explanation Formal definitions, alternate representations, and uses of odds and odds ratios (like a 1 : 2 chance of drawing a red ball vs. green ball from a barrel). - Alexei Andreev
- Probability The degree to which someone believes something, measured on a scale from 0 to 1, allowing us to do math to it. - Eliezer Yudkowsky
  - Conditional probability The notation for writing "The probability that someone has green eyes, if we know that they have red hair." - Eliezer Yudkowsky
    - Conditional probability: Refresher Is P(yellow | banana) the probability that a banana is yellow, or the probability that a yellow thing is a banana? - Nate Soares
  - Interpretations of "probability" What does it *mean* to say that a fair coin has a 50% probability of coming up heads? - Nate Soares
    - Correspondence visualizations for different interpretations of "probability" Let's say you have a model which says a particular coin is 70% likely to be heads. How should we as… - Nate Soares
    - Probability interpretations: Examples Consider evaluating, in June of 2016, the question: "What is the probability of Hillary Clinton wi… - Nate Soares
    - Subjective probability Probability is in the mind, not in the environment. If you don't know whether a coin came up heads or tails, that's a fact about you, not a fact about the coin. - Eliezer Yudkowsky
      - Probability distribution: Motivated definition People keep writing things like P(sick)=0.3. What does this mean, on a technical level? - Nate Soares
  - Joint probability The notation for writing the chance that both X and Y are true. - Eliezer Yudkowsky
  - Report likelihoods, not p-values If scientists reported likelihood functions instead of p-values, this could help science avoid p-ha… - Nate Soares
    - Likelihood functions, p-values, and the replication crisis What's the whole Bayesian-vs.-frequentist debate about? - Eliezer Yudkowsky
    - Report likelihoods not p-values: FAQ This page answers frequently asked questions about the Report likelihoods, not p-values proposal for… - Nate Soares
- Probability distribution (countable sample space) A function assigning a probability to each point in the sample space. - Tsvi BT
- Probability distribution: Motivated definition People keep writing things like P(sick)=0.3. What does this mean, on a technical level? - Nate Soares
- Sample space The set of possible things that could happen in a part of the world that you are uncertain about. - Tsvi BT
  - Sample spaces are too large Sample spaces are often large, so it is hard to do probabilistic computations using a raw distribution over the sample space. - Tsvi BT
  - Uncountable sample spaces are way too large We can't define probability distributions over uncountable sample spaces by just assigning numbers to each point in the sample space. - Tsvi BT
- Square visualization of probabilities on two events $$ \newcommand{\true}{\text{True}} \newcommand{\false}{\text{False}} \newcommand{\bP}{\mathbb{P}} … - Tsvi BT
  - Square visualization of probabilities on two events: (example) Diseasitis But it *seems* like the patient with the black tongue depressor has diseasitis... - Tsvi BT
- Two independent events What do [a pair of dice], [a pair of coins], and [a pair of people on opposite sides of the planet] all have in common? - Tsvi BT
  - Two independent events: Square visualization $$ \newcommand{\true}{\text{True}} \newcommand{\false}{\text{False}} \newcommand{\bP}{\mathbb{P}} … - Tsvi BT
- Well-calibrated probabilities Even if you're fairly ignorant, you can still strive to ensure that when you say "70% probability", it's true 70% of the time. - Eliezer Yudkowsky